Physics 2111
Unit 20
Today’s Concepts:
a) Static Equilibrium
b) Potential Energy & Stability
Mechanics Lecture 18, Slide 1
Example 20.1 (Painter on a Ladder)
Bill (mass m=75kg) is climbing a ladder (length L=2.5m, mass
M=50kg) that leans against a smooth wall (no friction between
wall and ladder). A frictional force f between the ladder and the
floor keeps it from slipping. The angle between the ladder and
the ground is q=70o.
L
What is the frictional force, f, between the ground
and the ladder if Bill is 0.5m up the ladder?
Bill
f
M
m
y
x
f
q
Mechanics Lecture 18, Slide 2
Balance forces:
x:
y:
Fwall = f
N = Mg + mg
Fwall
Balance torques:
L/2
L
mgd cos q + Mg cos q  Fwall L sin q = 0
2
 d Mg 
Fwall =  mg +
 cot q
L 2 

axis
Fwall = f
 d Mg 
f =  mg +
 cot q
 L 2 
Mg
d
mg
q
f
y
N
x
Mechanics Lecture 18, Slide 3
CheckPoint
In which of the static cases shown below is the tension in
the supporting wire bigger? In both cases the red strut has
the same mass and length.
A) Case 1
B) Case 2
T1
C) Same
T2
300
300
L
L/2
M
Case 1
Case 2
Mechanics Lecture 18, Slide 5
Example 20.2 (accelerating truck)
A 70kg box is loaded on the back of a truck. The box has a
height of h=1.2 meter and a width of w=0.8m.
a) What is the greatest rate at which the truck can accelerate
and still not have the box tip over?
b) At this rate, what would the coefficient of static friction have
to be to keep the box from sliding off?
Mechanics Lecture 18, Slide 6
Example 20.3 (hanging meter stick)
A meter stick with a mass of 150g hangs by two strings, one attached
at 25cm and the other attached at 75cm. Now the right string is cut.
a) What is the initial angular acceleration of the meter stick?
b) What the tension in the left string just after the string is cut?
Mechanics Lecture 18, Slide 7
These are the quantities we want to find:
ACM
T1
a
M
d
Mg
y
x
Mechanics Lecture 18, Slide 8
Apply
F
ext
= MACM
ACM = da
Mg  T1 = MACM
T1 = Mg  MACM
ACM
T1
a
M
Apply

ext
= Ia
ACM
Mgd = Ia = I
d
ACM
Md 2
=g
I
d
Mg
y
x
Use ACM = da to find a
Plug this into the expression for T1
Mechanics Lecture 18, Slide 9
Example 20.4 (hanging meter stick II)
A meter stick with a mass of 150g hangs by two strings, one attached
at 25cm and the other attached at 75cm. The right string is cut.
a) What is total acceleration of the center of mass when the stick is
vertical?
b) What is the tension in the string when the stick is vertical?
Mechanics Lecture 18, Slide 10
After the right string is cut, the meterstick swings down to where it is vertical for an
instant before it swings back up in the other direction.
What is the angular speed when the meter stick is vertical?
Conserve energy:
1 2
Mgd = I 
2
2Mgd
=
I
SFy=may = m2r
T
M

d
y
x
Mechanics Lecture 18, Slide 11
CheckPoint
Suppose you hang one end of a beam from the ceiling by a rope
and the bottom of the beam rests on a frictionless sheet of ice.
The center of mass of the beam is marked with an black spot.
Which of the following configurations best represents the
equilibrium condition of this setup?
A)
B)
C)
Mechanics Lecture 18, Slide 12
Stability & Potential Energy
footprint
footprint
Mechanics Lecture 18, Slide 13